44 
wrote these down word for word from the lips of the nar- 
-rators in their native tongue, and at his leisure afterwards 
translated them into English. Some of them were ob- 
tained by the distinguished folk-lorist and poet, Charles 
G. Leland, and published in his ‘‘Algonquin Legends.” 
A much larger collection of them, filling a volume of 452 
pages, has just appeared in the Wellesley College Philolo- 
gical Publications, entitled ‘‘Legends of the Micmacs,” 
with a most satisfactory preface by Miss Helen L. 
Webster. It is a work the reading of which is both de- 
lightful and instructive, and it leads ts far into the psy- 
chology of these children of nature. The original Mic- 
mac of most of these tales is still in existence, and should 
some day be printed for its linguistic value. 
PLEA FOR TEACHING THE HISTORY OF 
MATHEMATICS. 
BY JOSEPH V. COLLINS, PH.D., WOOSTOR, OHIO. 
Tue time alloted in our schools for the study of political 
and general history, as is well known, is all too short. 
Doubtless many teachers on seeing the title above would 
be disposed to say that it is well enough, but how can the 
teacher of mathematics find time for it ? And, besides, if 
a little history is a good thing in the mathematics, why 
would it not be equally desirable in language and science ? 
A fair answer to the latter question presents itself, viz. : 
Perhaps it would. 
It is not surprising that the history of mathematics is 
neglected in the common schools, because the normal and 
training schools do not concern themselves with it. The 
latter have some excuse for this course, since the colleges, 
from whence they draw their teachers, either pay no 
attention to it, or only the scantiest, and that indirectly. 
It is fair tosuppose that in a large number of cases the 
college student of to-day gets his knowledge of Greek 
mathematics, not from the mathematical department, but 
out of his Greek studies, and ina crude and confused form. 
He knows, or, of course, ought to know, that the elemen- 
tary geometries in use now are merely Euclid’s in substance, 
superior to Euclid’s in some ways, but in others less logical. 
If he were asked to describe the Greek mathematics, 
or to tell when algebra was first cultivated, it is doubt- 
ful whether he could give any satisfactory answer. 
Indeed, some very interesting statistics could no doubt be 
secured if these and a few other like questions were put to 
the seniors in our various colleges. It is doubtful whether 
the majority would know whether algebra was studied 
first in the fourth or fourteenth century, or whether trig- 
onometry was cultivated for its own sake at first or as an 
auxiliary to another science, and if the latter, what science ? 
That effect, whether great or small, the invention of 
cartesian co-ordinates had on the development of geome- 
try ? Whether our present notation in algebra was fixed 
by a few or by many hands? Or the answers to numerous 
questions as important asthese. Those who had traversed 
the ground of a good history, besides securing a much 
clearer comprehension of subjects they had taken years to 
learn, would have become acquainted with the evolution 
of a branch of science from humble beginnings and with 
slow steps, and indirectly would have had a good side- 
light thrown on general history. 
Even in our universities, if one may judge by the courses 
set fourth in their catalogues, there is no distinct pro- 
vision or requirement to securea knowledge of the history 
of mathematics, and so zt would seem just to charge neglect 
of the historical and unifying side of the study of mathematics al! 
along the line of our educational system. Of course there 
are exceptions to this. Cajori in his ‘‘ History and Teach- 
ing of Mathematics in the United States ” (page 163) says : 
SCIENG@E, 
Vol. XXIII. No. 573 
“One feature of the mathematical instruction at this in- 
stitution [ Princeton] that has been in vogue during the last 
ten years (perhaps longer) is, we think, to be recommended 
for more general adoption. Considerable attention is given 
to the study of the history of mathematics. The writer 
has before him examination papers, written in answer to 
questions set by Halsted in 1881. From the answers we 
infer that questions like these were asked : Who wrote the 
first algebra that has come down to us? What was its 
nature ? What part did the Hindoos play in the develop- 
“ment of algebra? Its growth during the Renaissance ? 
The laws underlying ordinary algebra? etc.’ The same 
book gives the following in the mathematical courses in 
the University of Texas, where Professer Halsted now is : 
“In the higher classes will be discussed the history and 
logical structure of the mathematical sciences.” Lectures 
on the history of mathematics are given also at the Uni- 
versity of Virginia. No doubt other instances might be 
found of historical courses offered, but on the whole this 
is the exception. It seems scarcely necessary to criticise 
this condition of affairs, as 1 presume almost anyone would 
agree that it is unfortunate. It is likely that it is due to 
the fact that each professor is a specialist and is unwilling 
to take from his own work the time necessary to prepare 
such a general course. 
The present seems an opportune time to bring forward 
the claims of this special study, since a new history of 
mathematics by an American author (Professor Cajori) is 
soon to appear from the press of Macmillan & Co. So far 
as the writer knows, it will be the first of its kind to be 
brought out in this country. It is to be hoped that if the 
book proves worthy, which it no doubt will, it will havea - 
large sale among college professors, and also among © 
teachers of more elementary mathematics. It will be a 
mistake for the latter to conclude that they can make no 
use of such a book. For along with enlarging their views 
of mathematics, they will find many facts of interest, many 
old principles new to them, some ideas of prime impor- 
tance for the proper teaching of scientific geometry, al- 
gebra, trigonometry, and analytics, and much material— 
some stories, perhaps—that may be used to break the 
monotony of class-room routine. A teacher who does 
not know what was the controlling idea in the Greek 
geometry, or one who has never. appreciated the difficulty 
met with in the study of incommensurables, or in attaining 
a satisfactory theory of parallels, is hardly in position to 
teach elementary geometry as it should be taught. Many 
of the results of mathematics, dry and abstract though 
they may seem from one standpoint, are yet full of interest 
when viewed as a part of the development of the subject, 
or when the circumstances under which they were dis- 
covered are known. Sometimes a knowledge of the per- 
sonality of an author of a work, or a demonstration 
or problem, adds interest to its study. The stories 
concerning the legend over Plato’s door, Archimedes 
and the Roman soldier, and Newton’s apple, are not the 
only ones that may be related even of these men,— 
may their shades forgive us for having harped on them so 
long,—for one and perhaps two of them are apocryphal. 
But one of the best results of a study of this history by 
the teachers of elementary mathematics would be the en- 
larging of their mathematical horizon. ‘Too many even at 
the present time think that the mathematics‘that lies beyond 
a knowledge of the elements of the calculus as set forth 
in our ordinary college courses is of a transcendental and 
non-useful character. It is safe to say that by as much as 
a teacher’s vision is widened and clarified, by that much - 
is he made a more intelligent and capable instructor. We 
enter a plea therefore for a better knowledge of the history 
of mathematics, hoping thereby to secure a better know- - 
ledge and teaching of the subject itself. ; 
